B1135
Title: Multi-resolution approximation via flexible cumulative shrinkage processes: The CUSP-MRA prior
Authors: Francesco Denti - University of Padua (Italy) [presenting]
Abstract: Geostatistical analyses require careful consideration when selecting a model to represent the spatial dependence structure of the data. One critical decision is whether to adopt a stationary or nonstationary spatial process representation. While nonstationary processes offer flexibility in capturing the data-generating mechanisms, they often are computationally burdensome. A highly scalable solution for dealing with massive datasets is the recently introduced Multi-Resolution Approximation (MRA). This model approximates the original process by evaluating it over knots at multiple spatial resolutions, capturing progressively local characteristics of the covariance structure. Within a Bayesian framework, the mixture MRA extends the MRA by representing the spatial random effect via a basis function expansion with spike and slab priors on the coefficients. In the mixture MRA, the spike probability increases geometrically with the resolution level. The mixture MRA model is enhanced using cumulative shrinkage processes (CUSP), granting more flexibility for the induced regularization. The model allows for an unbounded number of layers a priori while permitting potentially aggressive shrinkage to prevent the introduction of unnecessary latent components. The flexibility offered by the CUSP enables the identification of small-scale, local stationarity regions, which serve as potential indicators for further investigation, suggesting areas of interest for more detailed analysis.
